LONDON, July 13 (Reuters) - Barclays boss Antony Jenkins faces one of the biggest tests of his leadership this month when he decides whether the bank, Britain’s third largest, should fight accusations it deceived and defrauded customers in the United States.

If Jenkins accepts the allegations, made in a lawsuit filed by New York’s Attorney General, he will face a dilemma arising from his pledge to jettison any business that does not fit into the bank’s new, squeaky-clean image.

But the U.S. trading desk at the centre of the allegations is part of Barclays’ equities business, an area it had planned to keep largely intact while shrinking its investment bank.

It comes at a time of mounting discontent among investors. Some say that after almost two years in the CEO hotseat Jenkins is failing to turn around both culture and performance.

Barclays’ shares are down around 9 percent, close to two-year lows, since the lawsuit was filed, compared with a 3.5 percent fall in European bank stocks in the same period. They have also underperformed their European peers since Jenkins was appointed in 2012.

“We are concerned about some of the revenue and cost trends and the pace of management implementation,” said Colin McLean, managing director of SVM Asset Management, which owns Barclays stock. “There’s a gap between the promises and the actual delivery, particularly on costs and bonuses,” he said.

RISKY BUSINESS

Fighting the allegations from the New York attorney general would be a high-risk gamble, as other banks have found when they have taken on the authorities. If the allegations are proven to be even partially true, Jenkins’s credibility as the man to lead Barclays out of its scandal-scarred past would be in tatters.

Investment banks’ in-house platforms for buying and selling shares, known as dark pools, are under investigation by authorities in the United States and Europe amid allegations they have been used to rip off some investors.

New York Attorney General Eric Schneiderman said in his lawsuit he had evidence that Barclays staff falsified marketing material and misled big institutional clients in an effort to grow its dark pool to increase revenues and bonuses.

He said that occurred from 2011 to as recently as April, some 20 months after Jenkins took the helm, unlike other conduct issues the bank has faced, which occurred before he became CEO.

Barclays has hired external lawyers to help it investigate the allegations, including Matthew Martens, formerly the chief litigator at the U.S. Securities and Exchange Commission. The bank has until around July 25 to decide whether or not to fight the charges.

Dark pools let institutional investors trade shares anonymously and only make trading data available afterwards, reducing the chance of information leaking about their trade orders.

Trading at the venues, rather than on formal stock exchanges, has swelled since 2007, and it is estimated that more than 40 percent of all U.S. equities trades are executed in one of the several dozen dark pools in operation.

Barclays’ dark pool, known as LX, is the second most active alternative trading system in the United States after Credit Suisse‘s, according to regulatory data. Other banks with big dark pools include UBS , Bank of America, Morgan Stanley, Deutsche Bank and Goldman Sachs.

LIQUIDITY PROFILING

Potentially most damaging in Schneiderman’s complaint is that Barclays lied to core institutional clients, such as pension funds and insurance companies.

U.S. asset manager Alliance Bernstein said it suspended activity with the LX dark pool after the lawsuit was filed, and more clients have pulled out, industry sources said.

Barclays has said it is conducting a full internal investigation into the allegations and had brought in outside help, but declined further comment.

Barclays grew its dark pool business aggressively from 2011, helped by a service called ‘Liquidity Profiling’.

Liquidity profiling allowed Barclays to group its clients in the dark pool depending on their trading behaviour, ranging from safe and passive trading long-term investors to aggressive high-frequency traders trying to exploit tiny price changes.

Some high-frequency traders try to get an edge from speed and technology to detect large orders coming in and trading ahead of them. As a result, the big institutional investors often want to avoid trading with them and Barclays’ liquidity profiling offered them that option.

But Schneiderman said Barclays did not exclude the aggressive traders from the pool, despite telling clients it would. It also excluded information about some high-frequency trading firms using LX in its marketing material and gave sensitive information to major high-frequency trading firms to increase their activity, Schneiderman said in his complaint.

“SAINT ANTONY”

Barclays LX had its origins at Lehman Brothers, the investment bank that collapsed in September 2008. Barclays’ purchase of Lehman’s U.S. arm was its platform to build an equities business, led by many former Lehman employees, including Bill White, its head of electronic equities trading.

White has been taken off his day-to-day role and is helping with the bank’s internal investigation, people familiar with the matter said. White declined to comment via a Barclays spokesman.

Jenkins, a retail banker, was propelled to CEO in August 2012 with a pledge to overhaul the hard-charging investment banking culture that had dominated Barclays under his predecessor Bob Diamond, after an interest rate rigging scandal cost the bank $450 million.

Barclays, like many banks, faces other regulatory probes into past wrongdoing, with an investigation into foreign exchange trading potentially most damaging. Michael Helsby, analyst at Bank of America, estimates Barclays faces possible litigation costs of 7.5 billion pounds in the next three years.

There are also concerns around the bank’s operating performance, analysts and investors said.

When Jenkins presented his first strategic plan in February 2013 he estimated income from the investment bank would hold steady at about 12 billion pounds by 2015, but analysts now forecast it will be less than 7 billion.

Equities brought in 2.7 billion pounds in revenues last year, up by almost a third from 2010 and lifting its share of the investment bank revenue to 25 percent from 15 percent.

The electronic equities business was likely to have brought in about $180-200 million a year, and had about 80-100 staff, mostly in the United States, one of the former staff said. Schneiderman’s complaint cited internal Barclays documents valuing the growth opportunity from pushing more orders into LX at between $37 million and $50 million per year.

The problem for Jenkins, given his pledge to cast off areas where conduct falls short, is that shutting electronic equities would be near impossible without damaging the rest of the equities operation, which is a low-margin business based on huge order flow, industry sources said.

Attempts to downsize it could also exacerbate tensions between former Lehman Brothers staff who dominate Barclays’ investment banking division in New York and their colleagues in London, and accelerate an exodus of U.S. investment bankers. (Additional reporting by Lionel Laurent and Nishant Kumar. Editing by Carmel Crimmins and Will Waterman)